Esri have started migrating to stronger encryption certificates utilising SHA-256 for basemaps via HTTPS - Previously it was using SHA-1. Esri will continue updating ArcGIS Online certificates over the next few months. This change should be transparent to most of our users.
One group of users that might run into issues are ArcPad users with Windows Mobile 6.5 and earlier. Many of those devices still don't support SHA-256, which means you will begin seeing an increase in the number of ArcGIS Online service endpoints you cannot access via HTTPS. If you are using such a device, please contact your hardware vendor to find out your vendor's patch plans. We will be posting more information about this using the Twitter handle @ArcGIS Online.